# Vertical force acting on a body attached to an end of a rod/string when the rod/string is at an angle with the vertical plane

I am finding it very hard to visualize as well as to end up with an equation, for a situation where a vertical force is applied on one end of a rod/string of which the other end is ocuppied by an object. If the rod/string happens to be at an angle $$\theta$$ with the horizontal plane(plank) when the force is applied, what will be the force felt by the object?

Edit: consider that the string/rod is attached to a horizontal plank and that plank is accelarated exactly upwards

• It's not clear what you mean without a drawing.
– nasu
Jul 30, 2021 at 14:16
• Mohammad. I had a typo in my answer. Fixed now. “Now you need to make zero net force Perpendicular to the direction of the string” is correct Jul 30, 2021 at 16:25
• No i had it right the first time. The object does not accelerate in the direction of the string. The forces added up in the direction of the string are therefore zero. The string can provide force along its direction, but the net forces along its direction are zero, because it doesnt move (accelerate) in that direction. Changing it back 🙄 Jul 30, 2021 at 17:40
• @MSKB, I am unable to understand your question. According to your picture, is the plank, the object here? And if so, shouldn't that picture flip vertically? Your description does not match your picture. Because you say that the angle is measured from the vertical. And why it should make an angle with the vertical if you exert the force vertically?
– ACB
Jul 30, 2021 at 18:01
• Then the ball is the object? And at what point you exert the force?
– ACB
Jul 30, 2021 at 18:05

A string can only provide force in its own direction as tension. So the tension force would be $$T \cos(37) \hat x + T \cos (37) \hat y$$ where $$T$$ is the total tension force, for now is unknown.

The vertical force is obviously $$-mg \hat y$$.

Now you need to make zero net force IN THE DIRECTION of the string (sentence corrected), because the object does not move (accelerate) in that direction so net force is zero. Think about those two vectors and try to come up with an equation, and write in comments. I’m not allowed to do it for you.

So in this case the magnitude of the component of gravity that acts along the direction of the string is equal to T. in some sense it creates the counterforce of tension.

If the board moves up we can set-up an inertial frame. Read this answer first: Non-inertial reference frame, a pendulum in an accelerating car

What we will do is make a reference frame from the point of view of the board, where we move with the board. Try something on that in the comments or in a new question.

• Comments are not for extended discussion; this conversation has been moved to chat.
– rob
Aug 1, 2021 at 1:12